A precise description of quantum gravity is provided by the Anti-de
Sitter/Conformal Field Theory correspondence and formulated as a quantum field
theory in one fewer spacetime dimensions. This duality has shed light on many
deep puzzles in quantum gravity, but the emergence of local physics on the
gravitational side remains rather mysterious. I will present recent work
explaining how this emergence can naturally be understood as a manifestation of
quantum error correction, an idea used to protect quantum information from
decoherence. I will use this new interpretation to make precise the deep
connection between entanglement and spacetime geometry, and explore the quantum
nature of black holes. This talk should be quite accessible to beginning
graduate students and assumes no background in gravity, field theory, or
quantum error correction.